Im working on a 16x13 deck for an above ground pool. The deck is only 4 1/2 feet off the ground and is mainly for getting in and out of the pool. My questions is, what size posts should I use, 4x4 or 6x6?

Use 6X6, they are so much stronger and look much better.

Both are adequate for that size deck, your determining factors here are what look you prefer and your budget. Either way you are looking at a minimum of 6 posts for proper support. And if possible I would reduce the deck to 16×12 it will save you a ton on material cost. Good luck with your project.